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Cyclotomic structure in the topological Hochschild homology of $DX$

Cary Malkiewich

Algebraic & Geometric Topology 17 (2017) 2307–2356

Let X be a finite CW complex, and let DX be its dual in the category of spectra. We demonstrate that the Poincaré/Koszul duality between THH(DX) and the free loop space Σ+LX is in fact a genuinely S1–equivariant duality that preserves the Cn–fixed points. Our proof uses an elementary but surprisingly useful rigidity theorem for the geometric fixed point functor ΦG of orthogonal G–spectra.

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topological Hochschild homology, cyclotomic spectra, multiplicative norm, geometric fixed points of orthogonal spectra
Mathematical Subject Classification 2010
Primary: 19D55, 55P43
Secondary: 55P25, 55P91
Received: 17 May 2016
Revised: 21 January 2017
Accepted: 16 February 2017
Published: 3 August 2017
Cary Malkiewich
Department of Mathematics
University of Illinois at Urbana-Champaign
Urbana, IL 61801
United States